Mercer wants to know her name/handle, and the nature of any communication she had with Iki. Basically he's being cautious, looking for holes in her story, making sure that cutting her loose won't come back to bite him - perhaps literally. He's not a trusting sort to begin with, but her being cagey about revealing her name makes his hackles stand up just a little.
Mercer would likely sleep in the van anyway. His lifestyle - Traveler - I figure is a mix of cheap motels and fast food supplemented by the not exactly occasional night spent in the van.
As for Iki, it's a sure bet he's already notified his employers that Mercer is alive, likely with photographic evidence, so there's not much to lose by letting them finish him off. "Them" being either the gangers or his employers. Though Mercer's not above using the same trick as the vamps and planting a tracker on him to see where he goes. Of course, Mercer's not yet aware that the vamps were using that trick IC I don't think, but it's the sort of thing he'd do.